OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..20
FORMULA
a(n) = Sum_{k>=1} (k^(n^2))/2^(k+1); this is the analog of the Dobinski formula.
Integral representation as n-th moment of a positive function on a positive half-axis, in Maple notation: a(n)=int(x^n*(sum(exp(-ln(x)^2/(4*ln(k))) / (2^k*sqrt(ln(k))), k=2..infinity)/(4*sqrt(Pi)*x)+Dirac(x-1)/4), x=0..infinity).
a(n) ~ (n^2)! / (2 * log(2)^(n^2 + 1)). - Vaclav Kotesovec, Jun 08 2021
MATHEMATICA
a[n_] := PolyLog[-n^2, 1/2]/2; a[0] = 1; Table[a[n], {n, 0, 7}] (* Jean-François Alcover, Mar 30 2016 *)
Table[Sum[k!*StirlingS2[n^2, k], {k, 0, n^2}], {n, 0, 10}] (* Vaclav Kotesovec, Jun 08 2021 *)
PROG
(PARI) a(n) = sum(k=0, n^2, k!*stirling(n^2, k, 2)); \\ Seiichi Manyama, Jan 17 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson, Mar 09 2002
STATUS
approved